A wave is represented by the equation y = 0.5 sin 0.4π(X - 60t), where the distance (X) is measured in centimetres and time (t) in seconds. What is the wavelength of the wave?
The general equation for a wave is given by y = Asin(k(x−vt)), where A is the amplitude, k is the wave number, v is the wave speed, and x and t are the position and time, respectively.
The wave number k is related to the wavelength λ by the equation k = \(\frac{2π}{λ}\)
In the given wave equation, y=0.5sin(0.4π(x−60t)), the wave number k is 0.4π.
Setting k = \(\frac{2π}{λ}\) equal to 0.4π and solving for λ gives:
λ = \(\frac{2π}{0.4π}\) = 5cm
So, the wavelength of the wave is 5 cm.
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